Maximum slope convolutional codes

The slope is an important distance parameter for a convolutional code. It can be used to obtain a lower bound on the active burst distance and in this respect essentially determines the error-correcting capability of the code. An upper bound on the slope of rate R = b/c convolutional codes is derived. A new family of convolutional codes, called the maximum slope (MS) code family, is introduced. Tables for rate R = 1/2 MS codes with memory 1 less than or equal to m less than or equal to 6 are presented. Additionally, some new rate R = (c - 1) / c, 3 less than or equal to -c less than or equal to 6, punctured convolutional codes with rate R = 1/2 optimum free distance (OFD) and MS mother codes are presented. Simulation results for the bit error performance of serially concatenated turbo codes with MS component codes are presented.